The Estimate of Amplitude and Phase of Harmonics in Power System using the Extended Kalman Filter

Mehrdad Ahmadi Kamarposhti, Ahmed Amin Ahmed Solyman


Nowadays, the amplitude of the harmonics in the power grid has increased unwittingly due to the increasing use of the nonlinear elements and power electronics. It has led to a significant reduction in power quality indicators. As a first step, the estimate of the amplitude, and the phase of the harmonics in the power grid are essential to resolve this problem. We use the Kalman filter to estimate the phase, and we use the minimal squared linear estimator to assess the amplitude. To test the aforementioned method, we use terminal test signals of the industrial charge consisting of the power converters and ignition coils. The results show that this algorithm has a high accuracy and estimation speed, and they confirm the proper performance in instantaneous tracking of the parameters.


Kalman filter; minimal squared linear; estimator; power grid harmonic phase; power quality


W.M. Grady, S. Santoso, “understanding power system harmonics”, IEEE power engineering review, Vol. 1, pp. 8-11, Nov. 2001.

R.G. Ellis, “Harmonic analysis of industrial powwr systems”, IEEE Trans. Industrial Applications, Vol. 32, pp. 417-421, March 1996.

V. Suresh Kumar, P.S. Kannan, “Harmonics-its sources, effects and remedial measures on modern textile industry”, in proc-2002 universities power engineering conference (UPEC), pp. 133-136, 2002.

V. Suresh Kumar, P.S. Kannan, “Harmonic studies in space vector PWM inverter drive system”, in proc-2004 IEEE power engineering conf, Vol. WB7.2, pp. 1-5, 2004.

T. Assaf, H. Henao, G.A. Capolino, “A special method for on-line computation of the harmonics of symmetrical components in induction machines”, European Transactions on electrical power, Vol. 15, Issue 3, pp. 203-216, 2005.

G.T. Heydt, “Identification of harmonic sources by a state estimation technique”, IEEE Transactions on power delivery, Vol. 4, No. 1, pp. 569-576, 1989.

A. Asheibi, D. Stirling, D. Sutano, “Analyzing harmonic motoring data using supervised and unsupervised learning”, IEEE Trans. On power delivery, Vol. 24, No. 1, PP. 293-301, 2009.

E. Gursoy, D. Neibur, “Harmonic load identification using complex independent component analysis”, IEEE Trans. On power delivery, Vol. 24, No. 1, pp. 285-292, 2009.

K. Hartana, G. Richards, “Constrained neural-network based identification of harmonic sources”, IEEE Trans. On industry applications, Vol. 29, No. 1, pp. 202-208, 1993.

Suresh Kumar, P.S. Kannan, D. Kavitha, “Optimal estimation of harmonics in power system using intelligent computing techniques”, Proceedings of international joint conference on neural networks, Orlando, Florida, USA, Aug. 12-17, 2007.

M. Gupta, S. Srivastana, J. Gupta, “A faster estimation algorithm applied to power quality problems”, International journal of engineering science and technology, Vol. 2, no.9, 2010.

P. K. Ray and B. Subudhi, “Ensemble-kalman-filter-based power system harmonic estimation,” IEEE transactions on instrumentation and measurement, vol. 61, no. 12, pp. 3216–3224, 2012.

S. Liu, “An adaptive kalman filter for dynamic estimation of harmonic signals,” 8th International Conference on Harmonics and Quality of Power, vol. 2. IEEE, pp. 636–640, 1998.

J. Yao, D. Di, G. Jiang, S. Gao, and H. Yan, “Real-time acceleration harmonics estimation for an electro-hydraulic servo shaking table using kalman filter with a linear model,” IEEE Transactions on Control Systems Technology, vol. 22, no. 2, pp. 794–800, 2014.

H. M. Beides and G. T. Heydt, “Dynamic state estimation of power system harmonics using kalman filter methodology,” IEEE Transactions on Power Delivery, vol. 6, no. 4, pp. 1663–1670, 1991.

S. Zhong and K.-S. Tam, “A frequency domain approach to characterize and analyze load profiles,” IEEE Transactions on Power Systems, vol. 27, no. 2, pp. 857–865, 2012.

H. Wen, J. Zhang, W. Yao, and L. Tang, “Fft-based amplitude estimation of power distribution systems signal distorted by harmonics and noise,” IEEE Transactions on Industrial Informatics, 2017.

H. C. Lin, “Inter-harmonic identification using group-harmonic weighting approach based on the fft,” IEEE Transactions on Power Electronics, vol. 23, no. 3, pp. 1309–1319, 2008.

F. Zhang, Z. Geng, and W. Yuan, “The algorithm of interpolating windowed fft for harmonic analysis of electric power system,” IEEE transactions on power delivery, vol. 16, no. 2, pp. 160–164, 2001.

C.-I. Chen and Y.-C. Chen, “Comparative study of harmonic and interharmonic estimation methods for stationary and time-varying signals,” IEEE Transactions on Industrial Electronics, vol. 61, no. 1, pp. 397–404, 2014.

A. Ferrero, S. Salicone, and S. Toscani, “A fast, simplified frequencydomain interpolation method for the evaluation of the frequency and amplitude of spectral components,” IEEE Transactions on Instrumentation and Measurement, vol. 60, no. 5, pp. 1579–1587, 2011.

J. Zhao, M. Netto, and L. Mili, “A robust iterated extended kalman filter for power system dynamic state estimation,” IEEE Transactions on Power Systems, vol. 32, no. 4, pp. 3205–3216, 2017.

S. Wang, J. Feng, and K. T. Chi, “Analysis of the characteristic of the kalman gain for 1-d chaotic maps in cubature kalman filter,” IEEE Signal Processing Letters, vol. 20, no. 3, pp. 229–232, 2013.

R. G. Brown, P. Y. Hwang et al., “Introduction to random signals and applied Kalman filtering,” New York, Wiley, vol. 3, 1992.

J. Reddy, P. K. Dash, R. Samantaray, and A. K. Moharana, “Fast tracking of power quality disturbance signals using an optimized unscented filter,” IEEE Transactions on Instrumentation and Measurement, vol. 58, no. 12, pp. 3943–3952, 2009.

F. Gustafsson and G. Hendeby, “Some relations between extended and unscented kalman filters,” IEEE Transactions on Signal Processing, vol. 60, no. 2, pp. 545–555, 2012.

I. Arasaratnam, S. Haykin, and R. J. Elliott, “Discrete-time nonlinear filtering algorithms using gauss–hermite quadrature,” Proceedings of the IEEE, vol. 95, no. 5, pp. 953–977, 2007.

X. Lu, L. Xie, H. Zhang, and W. Wang, “Robust kalman filtering for discrete-time systems with measurement delay,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 54, no. 6, pp. 522–526, 2007.

R. Zhan and J. Wan, “Iterated unscented kalman filter for passive target tracking,” IEEE Transactions on Aerospace and Electronic Systems, vol. 43, no. 3, 2007.

S. K. Singh, N. Sinha, A. K. Goswami, and N. Sinha, “Several variants of kalman filter algorithm for power system harmonic estimation,” International Journal of Electrical Power & Energy Systems, vol. 78, pp. 793–800, 2016.



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Bulletin of EEI Stats